Teaching oxidation states to neural networks

DFT+U+V provides a robust framework to mitigate self-interaction errors in materials with strongly localized d or f electrons - especially for systems where the electronic localization occurs alongside with substantial hybridization [1] - and to correctly predict oxidation states in mixed-valence systems [2]. This, in turn, allows to incorporate redox-awareness into machine-learned potentials. We show that a neural-network training that considers atoms with different oxidation states (as accurately predicted by DFT+U+V) as distinct species can identify the correct ground state and pattern of oxidation states for the redox elements present. This can be achieved through a combinatorial search for the lowest-energy configuration, and is shown to always recover correctly the DFT+U+V ground state. This advance brings the time- and length-scale advantages of machine-learned potentials to key technological applications (e.g., rechargeable batteries), which require an accurate description of the evolution of redox states.